Determining profile parameters of a structure using approximation and fine diffraction models in optical metrology

Abstract

Provided is a method for determining one or more profile parameters of a structure using an optical metrology model, the optical metrology model including a profile model, an approximation diffraction model, and a fine diffraction model. A simulated approximation diffraction signal is generated based on an approximation diffraction model of the structure. A set of difference diffraction signals is obtained by subtracting the simulated approximation diffraction signal from each of simulated fine diffraction signals and paired with the corresponding profile parameters. A machine learning system is trained using the pairs of difference diffraction signal and corresponding profile parameters. A measured diffraction signal adjusted by the simulated approximation diffraction signal is input into the trained machine learning system and generates the corresponding profile parameters.

1. A method of determining one or more profile parameters of a structure using an optical metrology model, the optical metrology model comprising a profile model, an approximation diffraction model, and a fine diffraction model, the method comprising:
 (a) developing a metrology model of a structure, the metrology model including a profile model, the profile model having profile parameters; 
 (b) optimizing the metrology model, the optimized metrology model including an optimized profile model, 
 (c) calculating a simulated approximation diffraction signal based on the approximation diffraction model of the structure; 
 (d) generating a set of simulated fine diffraction signals from a set of profile parameters, the simulated fine diffraction signals generated using the optimized profile model of the structure; 
 (e) calculating a set of difference diffraction signals by subtracting the simulated approximation diffraction signal from each of the simulated fine diffraction signals of the set of simulated fine diffraction signals and pairing each difference diffraction signal with the corresponding profile parameters; 
 (f) training a machine learning system using the pairs of difference diffraction signal and corresponding profile parameters, the machine learning system trained to process the difference diffraction signal as input and generate the profile parameters as output; 
 (g) subtracting the simulated approximation diffraction signal from a measured diffraction signal resulting in an adjusted measured diffraction signal; 
 (h) using the trained machine learning system, inputting the adjusted measured diffraction signal and generating profile parameters; and 
 (i) if one or more matching criteria are met, accessing at least one generated profile parameter. 
 
     
     
       2. The method of  claim 1  wherein the structure is a wafer structure. 
     
     
       3. The method of  claim 2  wherein the wafer structure is a grating or a repeating structure. 
     
     
       4. The method of  claim 1  wherein calculating the simulated approximation diffraction signal utilizes an approximation algorithm for the diffraction simulation. 
     
     
       5. The method of  claim 4  wherein the approximation algorithm for diffraction simulation uses effective medium theory. 
     
     
       6. The method of  claim 5  wherein the effective medium theory replaces a periodic structure or a repeating structure with an anisotropic homogenous medium with an effective permittivity. 
     
     
       7. The method of  claim 4  wherein approximation algorithm for diffraction simulation uses coherent potential approximation, random phase approximation or dynamical effective medium theory. 
     
     
       8. The method of  claim 1  wherein generating the set of simulated fine diffraction signals is performed using rigorous coupled-wave analysis, finite-difference, Green Function, or modal analysis. 
     
     
       9. The method of  claim 1  further comprising:
 (j) modifying the approximation diffraction model and/or approximation algorithm; 
 (k) iterating steps (c) through (h) until the one or more matching criteria are met. 
 
     
     
       10. The method of  claim 9  wherein modifying the approximation diffraction model and/or the approximation algorithm comprises modifying an approximation algorithm for diffraction simulation or switching from using effective medium theory to coherent potential approximation. 
     
     
       11. A computer-readable storage medium containing computer-executable instructions to a method for determining one or more profile parameters of a structure using optical metrology, comprising instructions for:
 (a) developing a metrology model of a structure, the metrology model including a profile model, the profile model having profile parameters; 
 (b) optimizing the metrology model, the optimized metrology model including an optimized profile model, 
 (c) calculating a simulated approximation diffraction signal based on an approximation diffraction model of the structure; 
 (d) generating a set of simulated fine diffraction signals from a set of profile parameters, the simulated fine diffraction signals generated using the optimized profile model of the structure; 
 (e) calculating a set of difference diffraction signal by subtracting the simulated approximation diffraction signal from each of the simulated fine diffraction signals of the set of simulated fine diffraction signals and pairing each difference diffraction signal with the corresponding profile parameters; 
 (f) training a machine learning system using the pairs of difference diffraction signal and corresponding profile parameters, the machine learning system trained to process the difference diffraction signal as input and generate the profile parameters as output; 
 (g) subtracting the simulated approximation diffraction signal from a measured diffraction signal resulting in an adjusted measured diffraction signal; 
 (h) using the trained machine learning system, inputting the adjusted measured diffraction signal and generating profile parameters; and 
 (i) if one or more matching criteria are met, accessing at least one generated profile parameter. 
 
     
     
       12. The computer-readable storage medium of  claim 11  wherein the structure is a wafer structure. 
     
     
       13. The computer-readable storage medium of  claim 12  wherein the wafer structure is a grating or a repeating structure. 
     
     
       14. The computer-readable storage medium of  claim 11  wherein calculating the simulated approximation diffraction signal utilizes an approximation algorithm for the diffraction simulation. 
     
     
       15. The computer-readable storage medium of  claim 14  wherein the approximation algorithm for diffraction simulation uses effective medium theory. 
     
     
       16. The computer-readable storage medium of  claim 15  wherein the effective medium theory replaces a periodic structure or a repeating structure with an anisotropic homogenous medium with an effective permittivity. 
     
     
       17. The computer-readable storage medium of  claim 14  wherein approximation algorithm for diffraction simulation uses coherent potential approximation, random phase approximation or dynamical effective medium theory. 
     
     
       18. The computer-readable storage medium of  claim 11  wherein generating the set of simulated fine diffraction signals is performed using rigorous coupled-wave analysis, finite-difference, Green Function, or modal analysis.